Muirfield, which hosts the Open this week, does not allow women to join.

Dawson, chief executive of the R&A, said: "Obviously the whole issue of gender and single-sex clubs has been pretty much beaten to death recently.

"We do, I assure you, understand this is a divisive issue. It's a subject we're finding increasingly difficult, to be honest."

Last three Open winners

2012: Ernie Els

2011: Darren Clarke

2010: Louis Oosthuizen

He added: "In recent months we've been at great pains to try to explain some of the facts about this matter. Single-sex clubs are in a very small minority in the UK. Half of them are women only, half of them are men only. They're perfectly legal."

Asked what was the difference between a male-only club and one that allowed whites only, Dawson said: "There's a massive difference between racial discrimination, anti-Semitism, where sectors of society are downtrodden and treated very badly."

He continued: "But on the Saturday morning when the guy gets up or the lady gets up and out of the marital bed, if you like, and goes off and plays golf with his chums and comes back in the afternoon, that's not on any kind of par with racial discrimination or anti-Semitism or any of these things."